Surgery of Cobordisms of K3-surfaces

Student: Mendelevich Asia

Supervisor: Vsevolod Shevchishin

Educational Programme: Mathematics (Master)

Year of Graduation: 2017

In this paper we construct the Heegaard diagram of a cobordism between two elliptic Lefschetz pencils and describe various types of surgeries of such cobordisms. In the case when the cobordism is constructed from a symplectomorphism of a $K3$-surface we try to find invariants of such a symplectomorphism which can be expressed in terms the Heegaard diagram and the surgery. This could lead to an example of a homotopically trivial symplectorphism of $K3$-surfaces which is not symplectically isotopic to identity, or in contrary, to a proof of triviality of homotopically trivial symplectomorphisms of $K3$-surfaces.

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